You are walking up a staircase that winds up to the top of a tall square tower. It ascends one side, then the next, then the next – and then suddenly you are right back where you started. This is the kind of problem people who are trapped in the geometrically impossible, yet still strangely plausible, worlds of MC Escher have to deal with all the time. In his mind-boggling creations, dimensions collide and normality dissolves. Looking into his pictures is like standing on the very edge of a cliff – and being right down at the bottom at the same time.
The Dutchman’s illusions have been famous and beloved since the 1950s, when spaced-out fans first started claiming to see hemp plants hidden in his art. And now we have Kaleidocycles, a Taschen book about the artist featuring paper puzzle kits that allow you to actually build his paradoxical structures at home, unlikely as that may seem. The tome has just been reissued in time for Christmas and the 50th anniversary of his death next year. His work does seem perfect for the festive season, given it’s all fun and games. Or at least that’s how it seems, initially.
Escher’s visionary flair did not just confine itself to art: he also intruded into the world of science. His profound yet impossible perspectives seem to prophesy the greatest tricks of virtual reality. Yet Maurits Cornelis Escher – born in Leeuwarden, a city north of Amsterdam, in 1898 – showed absolutely no aptitude for any academic subject at school. His father was a hydraulic engineer – an important job in a country with so much land reclaimed from the sea. Although he despaired of his son, he supported young Maurits in his studies at art college in Haarlem, and in his travels around southern Europe, where he spent years developing his style.
In the 1920s, Piet Mondrian and the De Stijl movement were taking Dutch art into pure abstraction. Escher, meanwhile, was in Italy – using traditional printmaking skills to depict timeless cities on picturesque hilltops. These designs would become the building blocks of his deceiving universe. A thickly inked engraving of St Peter’s that he made in 1935 takes a spectacular, god’s-eye view of the Vatican basilica’s vast interior from up inside the dome. We see tiny people on the floor far below, as columns plummet down towards them in rushing, scary perspective.
In this powerful engraving, you can clearly see the roots of Escher’s art. The work reveals his love of perspective, the method of depicting deep space and distance invented in Renaissance Italy. To the likes of Leonardo da Vinci, perspective was not just art but science. He filled his notebooks with sketches of buildings and landscapes, fascinated by this mathematical technique.
Earlier this year, a film called Escher: Journey into Infinity looked afresh at this artist, examining how he gained cult status in the US counterculture, with bootleg versions of his work appearing on T-shirts. As well as exploring his influences, which range from densely packed Italian hilltop towns to the music of Bach, we found out that Mick Jagger once wrote to Escher, asking him to create an album cover. Not only did the artist decline, he told the Rolling Stone off for addressing him by his first name.
A flat surface is just a flat surface. As soon as you depict something on it that seems to have depth and solidity, you are constructing an illusion. In Escher’s most mature and unsettling works, he takes that to extremes to orchestrate multi-dimensional crashes of alternate realities. In his 1953 picture Relativity, everything is drawn in strict perspective. The only trouble is there are three points of view looking towards three vanishing points (the point where lines that would be parallel in reality meet on the page). The artist called these “different worlds” and in one of them, a waiter walks down an upside-down staircase to serve al fresco diners, whose table is vertical. In another, lovers stroll in a garden in defiance of gravity. Only a flight of stairs that rises from the bottom of the picture is “the right way up”. Yet rotate the square image on its side and everything changes. A different world now becomes the real one.
Escher’s dive into the beauty of maths and science started when his eyes were opened by an art even older than that of the Renaissance. When he visited the Alhambra, the medieval Islamic palace that sprawls along a clifftop overlooking Granada in southern Spain, he was carried away on a magic carpet of inspiration. Its rooms were lined with brightly coloured tiles arranged in complex patterns, fitted together in lattices of mind-boggling symmetry, all inspired by Arab science. Mathematics calls this tessellation: the complete covering of a surface by interlocking shapes without any gaps. It is the glory of Andalusian Islamic art.
Escher was transfixed. He also felt challenged – as if he was looking on the work of rivals. He started drawing his own tessellated surfaces, but with a difference. While the Alhambra is full of abstract shapes, Escher set out to tessellate figurative images. Birds, fish, lizards, angels, devils – he fits together these repeated forms in hallucinatory flows that transform from one thing into another. Fish swim with wide open mouths under the sea while birds glide above: then you see the gaps between the birds are fish shaped, and vice versa. They meet at the sea’s surface in a dazzling metamorphosis.
Europe was heading into shadow as Escher saw the artistic light. Horrified at the thought of his sons being brought up under fascist ideology, he moved his family from Italy to Switzerland. They then moved to Belgium but, after his mother died and the country was seized by the Nazis, they returned to the Netherlands to be closer to family and to settle her inheritance. Escher despised the Nazis and refused to ever visit Germany.
So it is surely not a coincidence that he started revealing gaps in reality the very moment the world was being sucked into a black hole. In his 1938 print Day and Night, two flights of swans, black and white, tessellate as they fly in opposite directions across the border between day and night. Look longer and you realise the nocturnal and daylit landscapes are mirror images of the same European vista. Escher depicts an eerie symmetry between light and dark in the year of the Munich agreement, with the continent on a knife edge between war and peace.
In 1944, now back home in the Nazi-occupied Netherlands, it would fall to Escher to get into the home of his beloved Jewish art teacher Samuel Jessurun de Mesquita – to save as much art as he could. “The Mesquita family,” he would later write, “had been hauled out of bed and taken away. It must now be regarded as practically certain that S Jessurun de Mesquita, his wife and their son Jaap all perished in a German camp.”
Escher’s fantastic tessellations brought the maths of the Alhambra head to head with modern physics. Roger Penrose, who won the 2020 Nobel Prize for his pioneering work on black holes, encountered Escher’s art in the 1950s while at a conference in Amsterdam. He went home and tried drawing Escher-like conundrums, publishing a paper that unveiled two “impossible” objects: a staircase that loops on itself without going up, and a solid triangular structure that looks real yet is connected in a totally absurd way, with its three corners all seeming to push outward while actually being on the same plane.
When Escher saw these Escheresque objects, he responded with his own fantastic interpretations of the infinite staircase and the Penrose triangle. His 1960 print Ascending and Descending depicts cowled figures marching up and down a staircase atop a palace that just takes them back to where they started. In 1961’s Waterfall, he gives the same seductive depth and detail to a vision of a waterfall working a mill. After hitting the mill wheel, water flows along a flat, zig-zagging channel until – impossibly – it falls again. Escher explained it was based on the Penrose triangle. So, in the 1960s, this Dutch graphic artist who had failed at school was in dialogue with the most advanced mathematics around.
Another print shows angels and devils interlocking on a sphere-like surface, getting smaller as they approach the edges of the globe. While striking, it looks almost straightforwardly Escheresque – yet in his book Cycles of Time, Penrose uses this work to explain the non-Euclidean “hyperbolic” geometry behind a new theory of the cosmos. In the pantheon of art-and-science crossovers, this is an extraordinary achievement.
Art is another way of thinking about the universe. It can illustrate mathematical phenomena that few could follow any other way. Escher took two artistic traditions, Islamic abstraction and Renaissance perspective, and fused them. The result is a multiverse of delights with no correct way up or down. Escher proved that looking can be a magical kind of thinking.
